Fossil fuel based energy systems are the main contributor to global warming. As new regulations come into place, a transition towards a more sustainable energy system must be realised. Hydrogen usage is regarded as the key enabler of such systems. The heart of these hydrogen-based energy systems (HESs) is the hydrogen back-up system (HBS) which is responsible for the production, transport and storage of hydrogen. This study investigated how the power-to-gas efficiency of a HBS is governed by various sources and services. Two services are defined for the HES; Service 1: Constant hydrogen supply for the chemical industry. Service 2: Interruptible hydrogen supply as a fuel for power back-up. Both services can use a wind farm or the power grid as the source. A fully transient mathematical model of the system was built in Matlab Simulink. This model uses a rectifier and a PEM electrolyzer to convert the source power into hydrogen. A transport system, consisting of a pressure control station (PCS) and a 50 kilometre transmission pipeline, delivers the hydrogen to the salt cavern. Here, the hydrogen is injected into a 1000 metre deep cavern by a PCS and an injection pipeline. After a discharge pipeline, a third PCS is installed to adapt the hydrogen temperature and pressure for another 50 kilometre long transmission pipeline. A final PCS adapts the flow properties to the desired service values. All components are able to fully capture the intermittent nature of the cases. Historical data of the spot prices for power and wind speeds of 2017 are used for the sources and services. The resulting production and consumption profiles for 2017 were used to size the HBS for each case, ensuring full use of the cavern capacity without over- or underproduction. Simulations of the defined cases showed that the caverns only completed one full charge-discharge cycle during 2017, showing that all cases demand seasonal storage. The power-to-gas efficiency of both the grid-powered cases is 58%. The wind-powered cases show efficiencies of 44% and 41% for the chemical industry and the power back-up cases, respectively. The main conclusions as to why these difference are present are described below. Wind-powered HBSs lead to roughly 24 – 28% more power losses due to a mismatch between the wind farm power output and the PEME operational power input limits. The most significant losses occur during low wind speeds when the wind farm output is between zero and the minimum PEME operating power. The PEME efficiencies are in the range of 67.5 - 70.1%, making it the largest contributor to the total HBS losses. The transport and storage systems for all cases have an efficiency of roughly 95.0 - 95.5%. The efficiency of wind-powered PEMEs is 2.3 - 2.6 percentage points higher compared to grid-powered. The service has no significant effect on the efficiency as the service pressure for all cases is for large part of the year lower than the transport and storage pressure, resulting in negligible power requirements for the transport system.